Watching Billy Crystal’s stunningly sophisticated, powerfully heartfelt and altogether wonderful stage memoir, “700 Sundays,” I experienced that intensely familiar rush of sentimental feeling about a New York City that this native New Yorker never even got the chance to know.

Only a few years after my birth in 1961, the city began to rot away from the inside. My own beloved Upper West Side neighborhood became awash in crime, the subway system that fascinated me would soon be covered in monstrous graffiti and dirt was rapidly supplanting the grass in Central Park. Everything – even the richest neighborhoods – became grimy and kind of decrepit.

There were still echoes of the city as it was in the 1950s, the era when it was sparking on all cylinders. It was safe then – clean, well-run, solvent. Its great institutions – banks, Wall Street brokerages, white-shoe law firms and corporate headquarters – were governing the nation.

And its cultural offerings – from the highbrow precincts of Partisan Review magazine to the middlebrow thrills of Broadway musicals to the down-low cool of be-bop – represented an unparalleled flowering of American energy and talent.

But New York was also a far more intimate place then, with a decidedly human scale. Its commercial streetscape was dominated by small shops and family-owned businesses, and in the neighborhoods, people congregated on sidewalks while children played in the far less trafficked streets.

In “700 Sundays,” Crystal, who was born in 1948, bears witness to New York’s great blaze of glory.

He grew up outside the city, in Long Beach, he was the youngest in an utterly typical Jewish family – “we all have the same five relatives who jump from photo album to photo album,” he says as he projects pictures of his parents and grandparents, who do indeed look exactly like photographs from my own family scrapbook.

But while the family may have been typical, the family business was not. Crystal’s grandfather owned a small music store on 42nd Street near Grand Central Terminal where he sold equipment and sheet music. Billy’s uncle convinced the old man to start stocking jazz records and then to record jazz records. By the late ’40s, Crystal says, the Commodore label was the world’s third most successful mail-order business next to Sears Roebuck and Montgomery Ward.

This amazing business was run out of a record store nine feet wide – one of innumerable New York City small businesses that seemed as eccentric and original as so many of the city’s residents.

Despite the narrow quarters, the Commodore Music Shop became a world headquarters of coolness – so much so that little Billy saw his first movie at a Loews venue on Second Avenue in the East Village sitting on the lap of Billie Holiday.

This remarkable world of “Jews and jazz” – with Louis Armstrong attending family Passover seders – was layered onto an entirely average New York childhood.

At the age of 5, on his first trip into the city, Billy discovered that his father went daily to a coffee shop where he had “the usual.” Billy ordered “the usual” for himself as well – which, it turned out, was a buttered roll, a cup of coffee and a cigarette.

And of course there were the trips to Yankee Stadium, where 8-year-old Billy noticed that every man in the stadium was dressed exactly the way Jack Crystal was – white shirt, sleeves rolled up below the elbow, top button open with knit tie loose around the neck.

That image returns at the end of “700 Sundays,” when Crystal recounts a recurring dream of being reunited with his father in Grand Central Terminal – he and other orphaned sons surrounded by fathers in white shirtsleeves.

That costume was as significant as Crystal’s dream suggests. It represented a proper division between adulthood and boyhood – a division that we no longer recognize. Fathers wore white shirts and ties, even at ballgames, in Jack Crystal’s day. That’s what men did.

These days I, like every other 43-year-old man in America, wear the same kind of clothing on a weekend day that I wore when I was 16.

The New York City where I grew up in the 1960s and 1970s lost the sense of the division between parent and child that resonates in every second of “700 Sundays.” Authority evaporated here right around the time that Jack Crystal died suddenly and unfairly (only weeks before the assassination of Jack Kennedy).

There was no reason to believe that it could ever restore itself.

And yet it did restore itself, in the 1990s turnaround that has led New York into a new golden age – an age that proved itself even more golden when the city demonstrated its adult mettle following the terror attacks of 9/11.

Still, it’s impossible not to feel the loss of the city’s eccentricities, its human scale, as expressed by businesses like the Commodore Music Shop.

And it’s impossible not to feel that something more profound was lost when the rolled-up white shirtsleeves and ties passed into history.

There was about Jack Crystal, and other men of his era, a kind of moral seriousness that seems sadly lacking now – a moral seriousness Billy Crystal so surprisingly evokes in his surprising nightly triumph at the Broadhurst Theater.